The effective tensile and bending stiffness of nanotube fibers

We analyze the pure bending state, preliminarily considering the pure traction problem, for a fiber with circular cross-section composed by monodispersed Nano Tube (NT) segments, whose length is much lower than the length of the fiber, arranged in a cross-sectional square lattice, possibly inclined with respect to the bending plane. The proposed model accounts for the compliant shear coupling of the constituent NTs along their lateral contact surfaces, and considers that the position of each NT is offset with respect to the neighboring ones by a fixed distance. The shearing of the NTs permits their mobility in longitudinal direction, inducing an internal rearrangement, calculated through energy minimization, that affects the macroscopic response. With a micromacro approach, the internal actions in the whole fiber are calculated. We find that uniform axial macroscopic strain is associated with constant tensile normal force in the fiber and null moment; correspondingly, constant macroscopic curvature provides a constant bending moment in the plane of bending and null axial force. It is then possible to consider the NT fiber as an equivalent homogeneous beam, whose effective tensile and bending stiffness can be calculated, finding a dependence upon the aspect ratio of the fiber, the aspect ratio of the individual NTs and, more important, the offset of the NTs. The model permits to interpret recent experimental results.